Organizations: College of Information Science and Technology, Eastern Institute of Technology, Ningbo, P. R. China. · University of Maryland, USA. · School of Computer Science, University of Nottingham, UK. · The Hong Kong Polytechnic University, Hong Kong. · Xi’an Jiaotong-Liverpool University, China. · Eastern Institute of Technology, Ningbo, P. R. China.
In this paper, we present a Goal-Aware Uncertainty-Guided Exploration (GAUGE) framework for planner-conditioned active calibration of opaque quadruped velocity interfaces. Commercial quadrupeds commonly expose planar-velocity commands, but the underlying locomotion controller remains inaccessible and can produce systematic discrepancies between commanded and realized motion. A navigation planner typically uses a structured subset of the command envelope. GAUGE maintains a Bayesian command-to-motion model and selects authorized trials according to their expected reduction of posterior epistemic uncertainty under the planner-induced command distribution. The resulting posterior supports validation-based stopping, bounded inverse compensation, and task-relevant recalibration after detected interface shifts. In three controlled response families, GAUGE reaches the joint criterion for task-facing accuracy and uncertainty with fewer trials than passive, D-optimal, and task-agnostic alternatives. Across six held-out Isaac Sim navigation maps, it meets the declared noninferiority margins against dense calibration. Code is available at https://github.com/EurekaZang/CalibAgent.
Figures & tables
Fig. 1: GAUGE framework. (A) IVR, weighted by the planner-induced T , ranks untried commands in the finite pool C ; authorization selects the highest-ranked feasible command. Valid observations update the posterior. (B) The posterior supports bounded inversion. (C) Frozen μ , rj0 , and S support temporal shift detection. Recovery retains m , inflates Σ , and resumes (A) with the same T . Validation or hard budgets end calibration and recovery. All commands require authorization; the controller is fixed. Images are simulator captures.
Fig. 2: Core evidence for planner-conditioned acquisition. The independent unit is one of 20 paired seeds; the affine, dead-zone, and heteroscedastic response families are averaged within each seed. (a) Control-minus-task-IVR first-crossing trials for the joint RMSE ≤.04 and epistemic-variance ≤.0015 criterion; task IVR crosses at 18.7 trials on average. (b) Held-out task RMSE across fixed budgets, with the 24-trial acquisitions marked for the support test. (c) The same frozen 24-trial acquisitions re-evaluated under alternative command supports; positive values favor task IVR, while broad-uniform support reverses the ordering. Bands and error bars are paired 95% bootstrap intervals over seeds.
Fig. 3: Calibration and recovery under interface shifts. (a) Shift parameters; blue denotes row-normalized change magnitude. (b) Recovery dynamics; shading marks trials 4–9. (c–d) Independent early-effect and trial-12 estimates. Simulation intervals are paired 95% bootstrap intervals (30 seeds in b; 144 per shift in c–d). (e) Online calibration: bars show means; linked circles show matched commands. (f) Scheduled-hardware recovery: open circles show command contrasts, filled markers show block means, and spans show observed ranges. Positive contrasts favor GAUGE; hardware effects are descriptive.
Outcome
Count
Exact 95% interval
Worst p95 trials / s
False alarm
0/120
[0,.0303]
—
Detection
143–144/144
[.9619,.9998]
3.9 / 10.1
Recovery
141–144/144
[.9403,.9957]
9.0 / 46.8
TABLE I: Isaac Lab shift-monitor operating characteristics.
Fig. 4: Navigation after calibration. Top: overhead replays on six held-out Isaac Sim maps. Blue curves show executed trajectories; opacity increases with time. Bottom: (a) success counts; (b) raw-minus-GAUGE capped-time gain (60-s failure cap); (c) matched-budget RMSE contrasts; (d) noninferiority tests of GAUGE (12 trials) versus dense calibration (30 trials), with time-ratio and success-difference margins of 1.25 and −0.05 . Points and whiskers denote paired means and 95% bootstrap intervals over 72 seeds per map.
Fig. 5: Physical Go2 navigation records. (a–b) Long-exposure views of the route-specific GAUGE deployments on offset slalom and weighted arc. (c) A separate fixed-DRL-DCLP endurance-gait comparison in the same obstacle scene: the direct-interface rollout (left) contacts an obstacle, whereas the GAUGE-calibrated rollout (right) clears it. These physical panels are qualitative route-level records.
Department of Mathematics, National University of Kyiv-Mohyla Academy, Kyiv, Ukraine · Department of Multimedia Systems, National University of Kyiv-Mohyla Academy, Kyiv, Ukraine · Department of Computer Science, University of Turin, Turin, Italy
Amazon Fulfillment Technologies & Robotics, Westborough MA, USA. · University of Iowa, Iowa City, IA 52240. · Massachusetts Institute of Technology, Cambridge, MA 02139, USA.